Properties

Label 800.2.bp
Level $800$
Weight $2$
Character orbit 800.bp
Rep. character $\chi_{800}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $224$
Newform subspaces $3$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

Total New Old
Modular forms 1024 256 768
Cusp forms 896 224 672
Eisenstein series 128 32 96

Trace form

\( 224q + 16q^{3} - 20q^{9} + O(q^{10}) \) \( 224q + 16q^{3} - 20q^{9} + 12q^{11} - 12q^{17} + 20q^{19} - 20q^{25} + 28q^{27} - 4q^{33} + 40q^{35} - 12q^{41} + 48q^{43} + 32q^{51} - 28q^{57} + 20q^{59} - 20q^{65} - 8q^{67} - 36q^{73} - 40q^{75} + 12q^{81} - 24q^{83} - 120q^{89} + 12q^{91} + 44q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
800.2.bp.a \(8\) \(6.388\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(-10\) \(4\) \(q+(-1+\zeta_{20}+\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
800.2.bp.b \(8\) \(6.388\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(10\) \(-4\) \(q+(-1+\zeta_{20}+\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
800.2.bp.c \(208\) \(6.388\) None \(0\) \(16\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)